Power of Maths: Paper 1 – Answers
11. €6000; €2700 12. (a) €37 (b) €13∙91 (c) €20 (d) €70∙91 (e) €429∙09 13. (a) €2240 (b) €2373∙06 (c) €12 270 (d) €39 116∙94 yearly; €3259∙75 monthly 14. €48 000; €1933∙06 15. €57 490 16. (a) €68 644 (b) €2745∙76 (c) €45 432∙16
Chapter 12 Exercise 4 1. (a)
CP (€) SP (€)
100 180
150 300
Profi t (€)
50 120 % Profi t
66 2 __
3
Profi t margin
50 33 1 __
3 % 40%
250 312·50 62·50 25 20% 50·40 72 21·60 42·86 30% 72
160 (b)
CP (€) 100 172 170
SP (€) 75 87
100
Loss % Loss 25 85 70
25
49·4 41·2
2. (a) 20% (b) €1073∙52 3. 14∙3% 4. €446∙25 5. (a) €6210 (b) 76∙2% (c) 43∙2% 6. 20% 7. (a) €30 000 (b) €19 755∙09
Exercise 5
1. (a) €2131∙25 (b) €206∙72 (c) 4∙2% (d) 9∙3% (e) €277∙28 2. (a) €420 (b) €3780 (c) €1209∙60 (d) €4989∙60 (e) €103∙95 3. (a) €1350 (b) €13 425∙84 (c) €14 775∙84 (d) €1275∙84 (e) 3∙5% 4. (a) €4650 (b) €1046∙25 (c) €158∙23 (d) €7196∙25 5. €405 6. (a) (i) €10 300 (ii) €10 609 (iii) €10 927∙27 (b) (i) €25 625 (ii) €26 265∙63 (iii) €26 922∙27 7. (a) €10 302∙25 (b) €23 622∙32 8. (a) €20 665∙13 (b) €14 111∙17 9. (a) 1∙57% (b) 2∙4% 10. €10 250 11. €16 120 12. 4% 13. €28 295∙79 14. 1∙32% 15. 41∙4% 16. €26 520; €2∙50 17. €20 000 18. 5%, €2500 19. (a) €11 411∙66 (b) €10 710; Option 1 20. 5% 21. €2125 22. €45 999 23. 20% 24. (a) €13 500 (b) €12 150 25. 43∙75%
88 122·2 55% Revision Questions
1. (a) (i) €16∙20 (ii) 23∙5% (iii) 28% (b) (i) 20 days (ii) 15 days 2. (a) €10 506 (b) 2∙5% 3. (a) €1560 (b) 192% (c) €38 768∙06 (d) €51 660 (e) 25% 4. (a) (i) 4 hrs (ii) €475∙20 (iii) €21∙30 (b) €852 (c) €210∙80 (d) €147∙80 (e) €34∙08 (f ) €33∙37 (g) €636∙85 5. (a) €336 866∙63 (b) (i) 266 (ii) €26 600 (iii) 38∙7% (iv) €7140 6. (a) 34∙6 kg/m2 (b) 28∙7 kg/m2 (c) 17% (d) Mass = 183∙11 pounds, height = 66∙93 inches 7. (a) €1 = ₤0∙8394 (b) €655∙23 (c) €1 = ₤0∙7983 (d) ₤534∙86 8. (a) €571∙34 (b) 6∙5% (c) €2432 9. (a) (i) €50 000 (ii) €20 000 (b) –7500 euro/year (c) V = 50 000 – 7500t (d) 1 August 2016 (e) 20∙5% 10. (a) 8∙208 m2 (b) 377 tiles (c) 3∙2% (d) 10 boxes (e) 23 (f ) €1045∙50
Section 6 Chapter 13
Exercise 1 1. (a) 4 Re (b) –7 Re (c) −3 √
(f ) 9i Im (g) –5i Im (h) √ (k) √
(d) –9i Im (e) 16 √
___ 4 i Im (l) 3
__ 3
Exercise 2
1. (a) 2 + 3i, 2, 3 (b) 5 – 7i, 5, –7 (c) – 6 + 5i, – 6, 5 (d) –7 – 4i, –7, – 4 (e) 0 – 3i, 0, –3 (f ) 7 _
(g) 1 _
2 + 3 _
( j) − 1 ___
(c) 7 + 11i, 7, 11 (d) 3 + 7i, 3, 7 (e) 5 + 13i, 5, 13 (f ) –3 + 11i, –3, 11 (g) 0 – 5i, 0, –5 (h) – 6 + 9i, – 6, 9 (i) 7 – 2i, 7, –2 ( j) 11 – 5i, 11, –5 (k) –3 – 6i, –3, –6, (l) –7 – 9i, –7, –9 (m) –15 – 22i, –15, –22 (n) –3 + 0i, –3, 0 (o) –3 + 11i, –3, 11 (p) 5 – 22i, 5, –22 (q) √ (t) √
√ √
__ 7 − 3
__ 2 + 3i, √
_ 2 i, √
__ 2 , 3 (r) 3 + 2 √
__ 7 , − 3
_ 2 (u) (3 + y) – xi, 3 + y, – x
__ 3 i, 3, 2 √
__ 3 (s) − 1
_ 2 − i, − 1
(v) x + (y – 3)i, x, y – 3 3. (a) (x + 2) – 3i, x + 2, –3 (b) (x + 7) – 2i, x + 7, –2 (c) 7 + (x – 2)i, 7, x – 2 (d) y + (5 – x)i, y, 5 – x
347
__ 2
2 i, 1 _
2 , 3 _
+ 3 __
2 (h) −8 + 3 _
2 i, − 1 ___
__ 2
, 3 __
4 i, –8, 3 _
4 (i) √
__ 2 − √
3 + 0i, 7 _
__ 3 i, √
3 , 0
__ 2 , − √
__ 3
2 2. (a) 3 + 4 i, 3, 4 (b) 4 + 7i, 4, 7
__ 3 i Im (i) √
__ 2 Re (d) 4i Im (e) 7i Im
__ 2 i Im ( j) 1
__ 2 Re (f ) –9 Re (g) 18i Im
_ 4 i Im 2. (a) 7 Re (b) –9 Re (c) 7i Im
___ √
__ 7
3. (a) –i (b) 1 (c) i (d) –1 (e) 3 (f ) 2i (g) 3i (h) 4i (i) –1 ( j) –11i (k) 18i (l) i (m) 2i (n) 32i
i Im
_ 2 , –1
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